How do constraint and parenting interact with each other?
In the copy rotation constraint you say you have set the copy space as world->local, that means rotating CubeB on the global z-axis will rotate CubeA in it's local z-axis.

As you parented CubeA to CubeC and then rotated CubeC, Cube A is located below CubeC but you should also notice that as CubeC is rotated, CubeA is rotated using the CubeC location as the pivot point, this leads to the CubeA local z-axis now aligned to the global x-axis.

This leads to the local rotation that you now see, CubeA is still rotating on it's local z-axis but that is no longer aligned to the global z-axis, so it appears to rotate differently to CubeB.

If you use an object that is easier to see the orientation, what is happening will be clearer.